fitting 2d data set fit function is not working

Hi,

this is my data set and I wanted to try to get a fit for it.

well, did not work with

fit([x,y],z,'poly23');

first it said: Dimensions of matrices being concatenated are not consistent.

then I made x and y the same length and

it said: Y must be a column vector.

And now I am stack. help please.

thanks

Answer 1

[Thiago Henrique Gomes Lobato]

The problem is that your z data is defined in a grid while your x and y define only the vectors of this grid. If you first actually create the grid you will be able to create the model

[xmesh,ymesh] = meshgrid(x,y);
a = fit([xmesh(:),ymesh(:)],z(:),'poly23');
figure,surf(xmesh,ymesh,z),shading interp
hold on
plot3(xmesh(:),ymesh(:),  a([xmesh(:),ymesh(:)]),'*' )

[Asliddin Komilov]

thanks, meshgrid is new to me, I will do some reading.

what is the formula for the surface, why this one is not working:

axTc = a(1) + a(2) *x + a(3) *y + a(4) *x^2 + a(5) *x*y + a(6) *y^2 + a(7) *x^2*y + a(8) *x*y^2 + a(9) *y^3;

[Thiago Henrique Gomes Lobato]

a is your linear model, but you can't acess the coefficients as a(x), but rather: a.p00, a.p01,etc... You can check the equation by looking at the output of the model

a

     Linear model Poly23:
     a(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p21*x^2*y +
                     p12*x*y^2 + p03*y^3
     Coefficients (with 95% confidence bounds):
       p00 =      0.4365  (0.405, 0.4679)
       p10 =     0.02601  (0.01672, 0.0353)
       p01 =  -0.0005043  (-0.0008066, -0.000202)
       p20 =    -0.09332  (-0.09619, -0.09046)
       p11 =   0.0002262  (0.0001687, 0.0002837)
       p02 =   1.986e-08  (-9.467e-07, 9.865e-07)
       p21 =   -7.72e-07  (-9.884e-06, 8.34e-06)
       p12 =  -2.696e-08  (-1.176e-07, 6.368e-08)
       p03 =    8.97e-12  (-1.019e-09, 1.037e-09)

x and y must have the same length and you will need to use dot operators ( .*, .^) if you want to write the formula, although it is much easier to just give the x and y to your model as I did in the response.

Answer 2

[Asliddin Komilov]

thanks, it is perfect but the fit gives this warning:

Warning: Equation is badly conditioned. Remove repeated data points or try centering and scaling. 

does it influence the accuracy?

[Thiago Henrique Gomes Lobato]

Sometimes yes, but in your case no. In your case you got an equation that basically perfect fits your curve.

[Asliddin Komilov]

thank you